Ctrl+Shift+B, subdivides bevel instead of smoothing bevel. How do I smooth it?
I'll present you method based purely on quad topology.



It's a little bit manual work, but nothing is worth more then nice quad base topology.

Make sure you have enabled F2 addon in User Preferences as it will speed up last step. You certainly don't need it. It will be just easier.




Delete 3 bottom vertices.
Add a Circle and set Vertices to 8/12/16/20/24... and so on. Just to have straight horizontal vertices along Circle. I have used 16 in this example.
Scale it down approximately between existing shape then scale it up with Vertex Snap and hover closest vertex. I've done it holding CTRL while scaling.
Remove top part of the Circle.
W > Remove Doubles to "merge" Circle with existing shape.
Select 2 vertices on one chosen side right before empty face, move mouse cursor to the other side and hold F (F2 addon).


I have two other methods on my mind but this seems to be the cleanest one so far.